Lesson video

Hello.

How are you today? My name is Dr.

Shorrock, and I'm really excited to be learning with you today.

We are gonna have a lot of fun as we move through the learning together.

Today's lesson is from our unit order, compare, and calculate with numbers with up to eight digits.

This lesson is called Use Knowledge of the Composition of Seven-Digit Numbers to Solve Problems. As we move through the learning today, we are going to deepen our understanding of how we partition larger numbers using place value charts and counters and the Gattegno chart to help us.

We are also going to look at some problem-solving related to this place value.

Now, sometimes new learning can be difficult, but it's okay because I know if we work really hard together and I'm here to guide you, then we can be successful in our learning today.

Let's get started then, shall we? How can we use our knowledge of the composition of seven-digit numbers to solve problems? This is our key word from the learning today, and it's always useful to practise saying key words aloud.

Let's have a go at this together.

My turn, partition.

Your term.

Fantastic.

When we partition a value or object, we can split it up into smaller parts, and we can decompose numbers using standard or non-standard partitioning.

So today let's start our learning by looking at how we partition seven-digit numbers, and we have Aisha and Lucas to help us.

Aisha and Lucas are learning how to partition seven-digit numbers like this one.

I wonder if you can read that number.

That's right.

We can use a separated comma to help us, can't we? We've got 5,381,492.

And Lucas wants to know how can we partition such a large number? Well, good idea, Aisha.

Always good to represent something.

So let's represent this number in a place value chart.

Here's our place value chart, and we've represented the number.

Now, can you see the digit five? What's the value of that digit five? We can use the place value chart to help us, can't we? The value of the digit five is 5 million.

What about the value of the digit eight? Can you see the eight? That's right.

The value of the eight is 80,000.

What about the value of the digit four? The value of the digit four is 400.

What's the three worth? Hmm, the question has changed slightly there, hasn't it? But it really means the same thing.

So find that digit three in that number.

What's it worth? The three is worth three 100,000s, which is equivalent to 300,000.

What about the nine? What's the nine worth? Can you see the nine in the number? That's right.

The nine is worth nine 10s, and we say 90.

We can form an equation to partition this number, showing the value of each digit.

We've got 5,381,492 is composed of five millions, three 100,000, eight 10 thousands, 1,000, 400, 90, and 2.

So we have formed an equation to represent that partitioning.

And this is standard partitioning because we partitioned the number in accordance with the value of each digit.

And we can also represent this partitioning as a bar model to help us see those different parts.

As well as a place value chart, we can also use a Gattegno chart to help us represent partitioning of the numbers.

5,381,492.

Well, that's composed of 5 million, 300,000, 80,000, 1,000, 400, and 90, and 2.

And again, we can represent that partitioning as an equation.

5,381,492 is equal to 5 million, added to 300,000, added to 80,000, added to 1,490, and added to two.

Let's check your understanding with that.

Could you use this Gattegno chart and complete the equation to show the partitioning of this number? I'm not going to read it for you just yet.

Pause the video while you have a go, and when you are ready for the answer, press play.

How did you get on? Did you work out that 2,093,519 is composed of two millions, 90,000, 3000, 500, 10, and 8.

Well done.

Let's have a look at this.

Aisha has represented a number with place value counters, and they're groups and they're in place value order, and we can use those place value counters to form an equation like we did with the Gattegno chart and the place value chart.

We've got 1 million added to, well, there's two 100,000 isn't there? So we say 200,000.

There are three 10,000, so 30,000, 3,000, and 10.

So we can use these place value counters to help us form an equation, and then we can recombine the parts, and that will tell us what number Aisha has represented.

If we recombine the parts, we get 1,233,010.

Oh, what do you notice this time? Lucas has dropped the place value counters that he has, and so they're now randomly arranged.

Hmm, how can we form that equation now to determine what number he's represented? What could we do to help us? That's right.

We could put the alike counters together in groups and then form an equation to determine the number.

So we've sorted our counters now, they're in like groups, and they are now in place value order, and then we can form our equation, 1 million plus 200,000 plus 10,000 plus 100 plus 20 equals.

So if we recombine those, we get 1,210,120.

Let's check your understanding.

Could you look at these place value counters? Do you notice they're all scrambled up, aren't they? So that's a hint there, isn't there? How you could start? And then could you complete the equation to show the partitioning of this number that I'm not going to read to you just yet? Pause the video while you have a go.

You might want to go and grab some place value counters or draw them, if that helps.

And when you are ready to go through the answers, press play.

How did you get on? Did you complete the equation to show that this number, 3,022,030, is composed of 3 million added to 20,000, added to 2000, added to 30.

Well done.

It's your turn to practise now.

Could you use place value counters if you have them? If not, you can draw them.

Could you pick six to nine counters at random? So that just means by chance, lucky dip.

Then write an addition equation to show their sum, and repeat this at least two more times.

For part two, could you imagine that you have some place value counters.

If you've got some, you don't have to imagine.

You could use them.

For each power of 10, from one up to and including 1 million.

So that's 1, 10, 100, 1,000, 10,000, 100,000, and 1 million.

And using exactly six counters for part A, could you tell me what is the greatest number that you can make? For part B, what is the smallest number that you can make? For part C, make a number as near to 500,000 as possible.

And for Part D, make a number as near to 900,000 as possible.

For question three, if you have some place value counters, you can use them here.

If not, you can imagine that you have some place value counters.

Some show 1 million, and some show 1,000, and some show 1.

Could you choose any three counters and write all the different possible numbers that you can make? Work systematically, so you know when you have all the possibilities.

Pause the video while you have a go at all of those three questions, and when you are ready to go through the answers, press play.

How did you get on? Let's have a look.

Question one, you had to use place value counters or draw them if you didn't have any and pick six to nine counters at random, and write addition equations.

You might have picked some counters like this.

And then I wrote an addition equation to represent this.

I've got 1 million, 300,000s, 20,000, so that's two 10 thousands, a 1000, and a 10, and my sum was 1,321,010.

For question two, you can imagine or using, if you actually had some, some place value counters for each power of 10 from one up to and including 1 million.

And using exactly six counters, you had to make the greatest number possible.

And the greatest number that you can make, you might have figured out, was 6 million.

The smallest number you could make was six using six one's counters.

A number as close to 500,000 as possible, well, the nearest number you can make to 500,000 with six counters is 500,001.

You would use five 100,000 counters and one one counter.

For part D, you had to make a number as near to 900,000 as possible.

The nearest number you can make to 900,000 is 1,000,005 using one 1,000,000 and five ones counters.

You might have worked out that 1,000,005 is 100,005 away from 900,000.

For question three, you had some place value counters, some showing 1 million, some showing 1000, and some showing one.

You needed to choose any three counters and write all the different possible numbers you could make.

These are the possible numbers that you could make.

3, 3000, 3 million.

2001, 1002, 2,000,001, 2,001,000.

1,000,002, 1,001,001, 1,002,000.

How did you get on with those questions? Well done.

Fantastic learning so far.

I can see that you've really deepened your understanding of partitioning seven-digit numbers.

We're now going to move on now and look at some missing number problems. Lucas has partitioned a number and writes the equation.

Oops.

Aisha accidentally spills her drink on his work.

Oh dear.

What do you notice? How can they determine which number is missing? So we started with 6,340,921, and we need to figure out, after Lucas has partitioned a number, which part is missing.

Let's work systematically through the whole.

Good idea.

And we're gonna compare the whole to the parts.

We've got the digit six, and that represents 6 million.

We can see that in the whole, and we can see that in the part.

The digit three, well, that represents 300,000, and we can see it in the whole, but, ooh, it's not there in the parts, is it? So this is the missing part.

6,340,921 is composed of 6 million, 300,000, the missing part, 40,000, 900, 20, and 1.

Let's look at a different example.

We've got 614,529, and then we've got a missing part.

We've got 4000, 500, 20, and 9.

Hmm, do you notice something? What could the missing number or that missing part be? Ah, Lucas has noticed something.

Have you? This is a six-digit number.

We've got 614, 529, but there are only five parts.

There's the missing part, and there's 4000, 500, 20, and 9.

So that's only five parts.

Hmm, what does that mean? What does that tell us? That means two of those parts must be combined together.

So let's determine which are the missing parts.

If we can recombine the last four parts, we get 4,529.

What's the missing part then, do you think? That's right.

It's the value of the digit six and one that are missing.

The value of the six is 600,000, and the value of the one is 10,000.

If we recombine those, we get 610,000, and that must be the missing part.

Let's check your understanding with that.

What is the missing number in this equation? Got 4,302,915 equals 4 million, add something, add 900, add 10, add 5.

Is it A, 302, B, 2000, C, 300,000, and D, 302,000? Pause the video while you have a think about that.

Maybe chat to a friend about this.

When you're ready to hear the answer, press play.

How did you get on? Did you say it must be 302,000? But why? Well, let's have a look.

We've got the number 4,302,915.

We can see the value of the four is 4 million.

We can see that in the whole and in the part.

The three has a value of 300,000.

Hmm, we can't see that in the parts.

What about the two? It's got value of 2000.

That's missing as well.

Oh, but we can see the 900, the 10, and the five.

So actually, it's the digits three and two that are missing, and they have a value of 302,000.

So the missing part was 302,000.

The 300 and the 2000 parts had been combined.

Right, Aisha and Lucas are playing a game now.

They're playing zap the digit.

I wonder if you've ever played that.

It's quite a fun game.

They're starting with a number.

Oh, can you read that? That's right.

It's 1,983,204.

5, or five tenths.

They take it in terms to zap the digit from this number, and that means they want to remove the digit to get that number down to zero.

Lucas is going to zap the digit nine.

So what does he have to subtract if he wants to zap that nine? That's right.

The nine has a value of 900,000, so he needs to subtract 900,000.

And then you can see he has zapped the nine because we're now with 1,083,204.

5.

Aisha's going to zap the digit one.

What do you think she needs to subtract to be able to zap that digit one? That's right, it has a value of 1 million, so she needs to subtract 1 million.

And Aisha writes the next equation.

If she subtracts 1 million from 1,083,204.

5, the children are now left with 83,204.

5.

You can see how they're zapping this number, aren't they, to get to zero? Lucas is now going to zap two digits, the four and the five.

Well, what's the value of the four and the five? Well, they have a value of 45 tenths.

So Lucas needs to subtract 4.

5.

If he subtracts 4.

5, we are now left with 83,200.

Aisha is going to zap the digits eight and three.

What's the value of the eight and the three? Well, the eight and the three have a value of 83,000, so she needs to subtract 83,000.

And now the children are just left with 200.

Lucas is going to zap the digit two.

The two has a value of 200, so he needs to subtract 200, and then they're left with zero.

As Lucas says, "Well done.

Brilliant." They have zapped all the digits in this number.

They started with 1,983,204.

5, and they are left with zero by zapping all those digits.

This is a really fun game.

I think if you get chance, you should have a go at playing it.

Let's check your understanding with this.

True or false.

If we want to zap the three digit in this number, we need to subtract 300,000.

What do you think? Pause the video while you decide if it's true or false, and then press play when you are ready to hear.

How did you get on? Did you say that's false? But why is it false? Is it because the value of the three is 30,000, so we need to subtract 30,000 to zap that digit three? Or is it the value of the digit three is 3000? We need to subtract 3000 to zap the digit three.

Pause the video, maybe chat to someone about this and compare your reasons, and then, when you're ready to hear the answer, press play.

How did you get on? Did you realise it must be A, the value of the digit three in that number is 30,000.

We read the number as 1,430,298.

4, so the value of that digit three is 30,000.

So we needed to subtract 30,000 to be able to zap that digit three.

How did you get on? Well done.

It's your turn to practise now.

For question one, I'd like you to look at these whole numbers and their parts and fill in the missing numbers, so partition these numbers.

For question two, could you fill in the missing symbols, the inequality symbols less than or more than in this equation? So is 5,320,812 less than or more than the parts that you can see? And is 459,013 less than or more than the parts that you can see? For question three, have a go at these zap the digit games.

You could check your calculation using a calculator.

For part A, could you write a subtraction equation to zap the digit six from the number? Well, I'm not gonna read these numbers to you 'cause sometimes that gives you a clue because how you say it sometimes will give away the partitioning.

So I'll read the digits.

3,561,301.

For part B, could you write a subtraction equation to zap the digit two from the number 539.

25 For C, write a subtraction equation to zap the digit nine from the number 1,908,340.

And D, write a subtraction equation to zap the digit four from the number 1,142,319.

Pause the video while you have a go at all those questions.

When you're ready to go through the answers, press play.

How did you get on with those? Let's have a look.

For question one, you were asked to fill in the missing numbers.

3,400,305 is composed of 3 million, 400,000, 300, and 5.

923,516 is composed of 920,000, 3,000, 500, 10, and 6.

5,062,100 is composed of 5 million, 62,000, and 100.

Did you notice there how that part was combined? Two parts were combined there.

2,124,003, that's 2,124,000 and 3.

For question two, you had to fill in the missing symbols, less than or more than.

We've got 5,320,812.

Well, that must be less than because our parts are 5,300,000 and 40,000.

In the whole we had 20,000.

459,013 must be less than 200,000 plus 500 plus 200,000 plus 60,000 'cause you had to recombine those 100,000s, so in total you had 400,060.

You had six 10,000s, whereas in the original whole you only had five 10,000s.

For question three, when you had to zap the digit games, to zap the digit six from the number 3,561,301, you needed to subtract 60,000.

To zap the digit two from the number 539.

25, you needed to subtract 0.

2.

For part C, to zap the digit nine from the number 1,908,340, you needed to subtract 900,000.

And for Part D, you needed to zap the digit four.

And you did that by subtracting 40,000.

The value of the four was 40,000.

How did you get on with all those questions? Brilliant.

I am really impressed with how hard you have tried today, and that's really important in maths.

I can see you've made a lot of progress at using your knowledge of the composition of seven-digit numbers to solve problems. We know the digits in a number indicate its structure, so it can be decomposed into its parts.

Numbers can be decomposed or partitioned according to the values of their digits.

And missing parts can be determined by comparison of what you know, those known parts to the whole.

I have had great pleasure learning with you today, and I look forward to learning with you again soon.

Goodbye for now.